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Polygon Exterior Angle Sum Geometry 3-4b 2 1 Vertical Pair Review – Name the angle relationship 160° 20° Supplementary Angles Review – Name the angle relationship 2 1 Linear Pair Review – Name the angle relationship 35° 55° Complementary Angles Review – Name the angle relationship 2 1 Vertical Pair Review – Name the angle relationship 60° 30° Complementary Angles Review – Name the angle relationship 1 2 Linear Pair Review – Name the angle relationship 90° 90° Supplementary Angles Review – Name the angle relationship Any of the six angles inside the polygon What is an interior angle? When the sides of the polygon are extended, the angle that is adjacent to the interior angle What is an exterior angle? When the sides of the polygon are extended, the angle that is adjacent to the interior angle What is an exterior angle? Spot the exterior angle Which side do you extend to create an exterior angle? Exterior Angles Either one, these two angles are congruent, because they are vertical angles. Exterior Angles What is the value of all the exterior angles in any polygon? Exterior angle • Get your supplies – Printer Paper – Straightedge – Protractor Exterior Angle Investigation • Draw a large polygon on your paper Pentagon or larger • Extend each of its sides to form exterior angles Exterior Angle Investigation • Measure all of the interior angles except one. Write the value of the interior angle on the angle. • Use the polygon sum conjecture to calculate the measure of the last angle before you measure it. Exterior Angle Investigation • Use the linear pair conjecture to calculate the value of each exterior angle. • Write down the value on the angle • Add up all the exterior measures Exterior Angle Investigation • The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360° Polygon Exterior Angle Sum Theorem What is the measure of an exterior angle in a regular polygon? Exterior angle • The measure of each exterior angle of a regular n-gon is 360°/n Exterior Angle Theorem • You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: 180° - 360°/n (180°(n-2))/n Equiangular Polygon Conjecture • Pages 147 – 150 • 1 – 4, 47 – 49, 73 Homework
